class: center, middle, inverse, title-slide # Lecture 8 ## Hipothesis guided model comparison ### Psych 10 C ### University of California, Irvine ### 04/15/2022 --- ## Hypothesis as models - When we have one independent variable that can take more than 2 values comparing a Null model which assumes that every group has the same expected value with the effects model which assumes that every group has a different expected value is not enough to answer our research question. -- - This is because the Effects model can be the better than the null in multiple ways. -- - For example, the Effects model will account for the data better if it is true that: -- 1. If every group is different `\(\mu_1 \neq \mu_2 \neq \mu_3\)`. 2. If at least one group is different `\(\mu_1 = \mu_2 \neq \mu_3\)`. -- - Both of the previous statements are consistent whit the main assumption of the Effects model, which in isolation can only tell us that at least one group is different. --- ## Hypothesis as models - As we showed with the anxiety example, we can reach an answer to our research question by comparing multiple model, which assume that one group is different from the rest. We do this with each group one at a time. -- - When our independent variable can take only 3 different values, this resulted in us having to look at the predictions and errors of 5 different models. -- - If we increase the number of goups (or values of our independent variable) this number will increase rapidly. For example, if we have 4 groups the number of models that we could compare is 9, and for 5 it grows to 17. -- - We would prefer not to have to look at so many models every time we have more than two groups. -- - One way to reduce the number of models that we look at is by making our research question more precise. --- ## A better approach to comparing anxiety levels - Going back to wour anxiety levels example, instead of asking the question: -- - Are there any differences between the anxiety levels of First year students in the 218, 2019, and 2020 cohorts? -- - We could ask the question: -- - Are the anxiety levels of students from the 2020 cohort different from students in 2019 and 2018? -- - Notice that our new question is now centered around First year students on the 2020 cohort and not on differences between all cohorts. -- - In order to answer this question we only need to look at 3 models, first the Null, then the Effects and finally the 2020 model from last class. -- - Comparing Null and Effects model will tell us if there is at least one group that is different. Then our 2020 model will answer our actual question, Are the anxiety levels of First year students in the 2020 cohort different from students in the 2018 and 2019 cohorts? --- ## Hypothesis and models - Thus, just by redefining our experimental question we can reduce the number of comparisons that we have to make. -- - In the previous example our second question makes more sense as there is no real reason to assume that 2018 and 2019 should be different, however, due to the pandemic, we would expect First year students from the 2020 cohort to be more anxious than others. -- - One important thing to keep in mind is that we don't look for hypothesis that will reduce the number of models that we need to compare. A hypothesis should always come first. -- - In other words, we perform an experiment because we have a hypothesis regarding the outcomes of an experiment. This hypothesis will also inform our model comparisons. -- - As we mention before, this only becomes a problem when we have multiple groups and not when there are only two. --- class: inverse, center, middle # Example ## New treatment for blood preasure --- # Research problem: - A pharmaceutical company is about to launch a new drug as a treatment for high blood pressure -- - Before that, they have to show that their treatment works better than both a control substance (placebo) and the current standard of care (standard) treatment. -- - They have designed an experiment where participants are randomly assigned to one of three groups. There will be 25 participants assigned to each group for a total of 75. -- - Given our objective, which models would you consider for a comparison? .can-edit.key-likes[ Model 1: Model 2: Model 3: Model 4: Model 5: ] --- ## Experiment - For each participant the experimenters have recorded the blood pressure of each participant after 2 weeks of treatment. 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